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I'm a homeschool mom, my daughter is 7. She will be in second grade next year. I appreciate the different ways of doing math, rather than just stacking the numbers and adding/subtracting. I'm not sure how to go about teaching it. Any good resources out there for a homeschool parent? Thanks!

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  • $\begingroup$ Homeschooling varies wildly in all topics. Our family uses the site forums.welltrainedmind.com to get advice on math (and other subjects). $\endgroup$ – Aeryk Apr 26 '16 at 18:58
  • $\begingroup$ We use Singapore math for my kids. My wife has been very happy thus far. That said, there are a bunch of different versions so you'd want to do some research to decide which one fit your needs best. From what I've seen the curriculum is very conceptually oriented. It works towards concepts as opposed to solving standard template problems. My wife prefers it vastly to Saxon (who was an engineer and not a mathematician btw... this matters). $\endgroup$ – James S. Cook May 8 '16 at 20:46
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This is coming from an educator that isn't fond of common core for various reasons. What I believe is at the heart of common core math tho, is that the "Why?" is important. Math isn't just a series of steps to get to an arbitrary answer that someone says works, but it's a logical method of using order built into numbers to arrive at the correct answer.

My personal philosophy is that students first and foremost need the building blocks to USE to think. Ensure that they know their multiplication tables like their own name! But... once they have that foundation on which to think, give them all the "why's" you can; not just "these are the steps." My 2 cents anyway.

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  • $\begingroup$ this feels more like a comment, what you say is insightful but it does not in any way answer the question about resources... $\endgroup$ – celeriko May 2 '16 at 12:23
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    $\begingroup$ @celeriko True. I see what you're saying. I guess I was addressing the unstated question, "I'm not sure how to go about teaching Common Core math" (As this was in the original post before editing). I felt a generic "How can I better teach common core math" deserved the more generic answer rather than giving a website that may or may not cater to her specific curriculum and math experience level as a homeschool parent. $\endgroup$ – Elem-Teach-w-Bach-n-Math-Ed May 2 '16 at 22:04
  • $\begingroup$ Some students work better the way you describe, and others have trouble with memorizing multiplication tables, and do better having that on a card to look up while they do all the other math that uses that. $\endgroup$ – Sue VanHattum May 2 '16 at 22:12
  • $\begingroup$ Granted I've only been teaching for 5 years, I'd hardly count myself any sort of expert, but I've found that with about 2 min. of flash cards at the beginning of math class 3 days/week, most 4th graders have them down pat; the very few others do so by the end of 5th. By this point in the year, I've set them aside except as a reward (yep, you read that right) where I also give them "-7" or something similar to do before giving the answer. They're now able to do massive long division problems with little to no difficulty/mistakes, have great confidence in math, and even look forward to it! $\endgroup$ – Elem-Teach-w-Bach-n-Math-Ed May 2 '16 at 23:06
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I rather like The Art of Problem Solving's Beast Academy series. It is a complete curriculum, but in a "graphic novel" format, with problem solving emphasis. This can lead into other resources from AOPS for middle and high school. (I was myself homeschooled, homeschool both of my children ages 5 and 8, and am a mathematics professor. In my experience, the perspective of these books will begin to develop the sort of attitude toward mathematics that yields playful and productive discovery, as well as the development of core skills.)

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Stacking the numbers, and carrying the tens, works and is understandable to generations of people. You can explain each step as being correct by itself.

I recommend teaching your daughter how to count on her fingers using roman numerals. This will let her see how she can "carry the one". Her four fingers on her right hand are Is; her right thumb is a V; her four fingers on her left hand are Xes; and her left thumb is an L.

Whatever method you teach, you should make sure that every step has a clear meaning, and that it is clear why the expression at that step has the same value as the expression at the previous step. You should make sure that your daughter can explain each step.

Addition example

            1        1      1 1      1 1
  537      537      537      537      537
+ 547 => + 547 => + 547 => + 547 => + 547
 ====     ====     ====     ====     ====
             4       84      084     1084

In the first step, 7 + 7 = 14. She can check this by doing the math on her fingers (using roman numerals). The 4 goes down below, and the 10 is "carried", by putting a 1 above the tens place.

In the second step, 1 + 3 + 4 = 8. (or 10 + 30 + 40 = 80, because all three numbers are in the tens place.) The 8 goes down below. Because 8 is less than 10, there is no need to carry anything from this step.

In the third step, 5 + 5 = 10. (or 500 + 500 = 1,000, because both 5s are in the hundreds place.) The 0 goes down below, and the 10 is "carried", by putting the 1 above the thousands place.

In the fourth step, 1 + 0 + 0 = 1. (or 1,000 + 0 + 0 = 1,000, because this step is for the thousands place.) The 1 goes down below, and nothing needs to be carried further.

Teach your daughter to check her own work.

  • Casting out nines is an old-fashioned way.
  • Performing the inverse calculation is a complete way -- but might allow making the same mistake in reverse.

Teach your daughter to sanity check her own work.

  • Estimating checks the rough size of the answer.

Have your daughter keep a log of her most common mistakes

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There are so many mathematical directions you can go. I have found Living Math Forum (a yahoo group) to be incredibly eye-opening. There are about 5,000 members, and questions usually get a variety of answers from other homeschoolers.

How do you want to approach math? There are various curricula available, there are "math readers", there are activities that help kids make sense of the math, and activities that make it feel useful to them.

And how comfortable with math are you?

My answers to you would depend very much on details of your situation and interests.

You also might be interested in my book, Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers.

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After three years of intensive work with the new math standards (as part of the writing team for a new, national common core-based mathematics curriculum), my partner and I began consulting for school districts, training their teachers in the very thing you inquired about....HOW best to teach this new math. Almost without exception the teachers we worked with asked one common question..."How can we help our students' parents?" It seemed as though nothing existed (yet) that would work with ANY curriculum to simplify the process of TEACHING it....to basically just help parents navigate these new waters in a way that made them feel confident. After much searching, for a resource we could recommend, we found we needed to create it.

In response to all of the parents and teachers (and PARENTS WHO TEACH!!) we created the "Thinking Math Differently" series of guide books. Each level-specific book will work alongside any curriculum you are using, enabling you to 1. gain your own understanding of each topic and 2. develop your own style of teaching it that will foster deep understanding in your child.

These guides, available on Amazon.com, are a true resource for teaching elementary mathematics! Please feel free to reach out with any specific questions you may still have! Our email address is conceptuallearningassociates@gmail.com.

https://smile.amazon.com/Thinking-Math-Differently-Essential-Teachers/dp/0997789263/ref=sr_1_4?ie=UTF8&qid=1499974944&sr=8-4&keywords=Thinking+Math+Differently

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    $\begingroup$ First, it is very nice you have a link through smile.amazon.com. Second, I am disappointed there is no content in the preview of the books I clicked on. It seems it just lets me see the front matter and a couple back pages. I can't see any substantive sections with actual math. Do you have a sample of the books which contains something more from the middle? $\endgroup$ – James S. Cook Jul 14 '17 at 0:33
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    $\begingroup$ I'd like to second the request for more information about what is inside the books, otherwise this is an advertisement that doesn't feel like it fits very well on the matheducators site. $\endgroup$ – Chris Cunningham Jul 14 '17 at 2:56
  • $\begingroup$ I'm so sorry for the late reply to your comments! I, too, was disappointed that only the front matter is preview-able. This is something we are still trying to work on. We have, however, created an electronic sample of the books...with one chapter from each of the books...to address this issue. Please email to the address in my original post and I will be happy to sent it to you! $\endgroup$ – Patti J Dieck Jul 16 '17 at 22:18
  • $\begingroup$ I do apologize for my post sounding like an advertisement..I realize in hindsight how it does seem like that. Really, though, we only wish to be of assistance...to help clear up some of the mystery of this "new math" for parents and others who didn't learn this way but must now teach it. The initial question asked was whether there were resources available...so I was really trying to answer that. I hope we were not offensive in any way. $\endgroup$ – Patti J Dieck Jul 16 '17 at 22:23

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